Topic #10 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor (email@example.com) Subject: Book on Orthogonal Polynomial for Exponential Weights [From the Springer Mathematics Newsletter] Forthcoming: A.L. Levin, The Open University of Israel, Tel Aviv, and Doron S. Lubinsky, Witwatersrand University, Wits, South Africa Orthogonal Polynomial for Exponential Weights CMS Books in Mathematics, Vol 4 2000. Approx. 350 pp. Hardcover $69.95 (tent.) ISBN 0-387-98941-2 The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. The use of potential theory since the early 1980's has had a dramatic influence on the development of orthogonal polynomials associated with weights on the real line. For many applications of orthogonal polynomials, for example in approximation theory and numerical analysis, it is not asymptotics but certain bounds that are most important. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel functions, Bernstein inequalities, restricted range inequalities, and record their bounds on the orthogonal polynomials as well as their asymptotic results. This book will be of interest to researchers in approximation theory and potential theory, as well as in some branches of engineering.